hdu 2955 Robberies（01背包）

Robberies

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 7288    Accepted Submission(s): 2737

Problem Description

The aspiring Roy the Robber has seen a lot of American movies, and knows that the bad guys usually gets caught in the end, often because they become too greedy. He has decided to work in the lucrative business of bank robbery only for a short while, before retiring to a comfortable job at a university.


For a few months now, Roy has been assessing the security of various banks and the amount of cash they hold. He wants to make a calculated risk, and grab as much money as possible.


His mother, Ola, has decided upon a tolerable probability of getting caught. She feels that he is safe enough if the banks he robs together give a probability less than this.

 

Input

The first line of input gives T, the number of cases. For each scenario, the first line of input gives a floating point number P, the probability Roy needs to be below, and an integer N, the number of banks he has plans for. Then follow N lines, where line j gives an integer Mj and a floating point number Pj . 
Bank j contains Mj millions, and the probability of getting caught from robbing it is Pj .

 

Output

For each test case, output a line with the maximum number of millions he can expect to get while the probability of getting caught is less than the limit set.

Notes and Constraints
0 < T <= 100
0.0 <= P <= 1.0
0 < N <= 100
0 < Mj <= 100
0.0 <= Pj <= 1.0
A bank goes bankrupt if it is robbed, and you may assume that all probabilities are independent as the police have very low funds.

 

Sample Input

30.04 31 0.022 0.033 0.050.06 32 0.032 0.033 0.050.10 31 0.032 0.023 0.05

 

Sample Output

246
题意：给出n个银行，每家银行有相应的钱Mj元，到每家打劫都有相应的被抓的概率Pj，求在被抓的概率不大于P的情况下，能抢劫到的最多的钱数。
思路：01背包的变形。可以讲被抓的概率转化为逃脱的概率，dp[i]表示抢到价值为i的钱时的最大逃脱概率。
AC代码:
#include <cstring>#include <string>#include <cstdio>#include <algorithm>#include <queue>#include <cmath>#include <vector>#include <cstdlib>#include <iostream>using namespace std;double dp[10005];double w[105];int v[105];int main(){    int n,t;    double p;    cin>>t;    while(t--)    {        memset(dp,0,sizeof(dp));        int sum=0;        cin>>p>>n;         p=1.0-p;        for(int i=0;i<n;i++)        {            cin>>v[i]>>w[i];            w[i]=1.0-w[i];            sum+=v[i];        }        dp[0]=1.0;        for(int i=0;i<n;i++)        for(int j=sum;j>=v[i];j--)        dp[j]=max(dp[j],dp[j-v[i]]*w[i]);        for(int i=sum;i>=0;i--)        if(dp[i]>p)        {            cout<<i<<endl;            break;        }    }    return 0;}